{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Case study: Hopper optimization\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# If you want the figures to appear in the notebook, \n",
    "# and you want to interact with them, use\n",
    "# %matplotlib notebook\n",
    "\n",
    "# If you want the figures to appear in the notebook, \n",
    "# and you don't want to interact with them, use\n",
    "# %matplotlib inline\n",
    "\n",
    "# If you want the figures to appear in separate windows, use\n",
    "# %matplotlib qt5\n",
    "\n",
    "# tempo switch from one to another, you have to select Kernel->Restart\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kg = UNITS.kilogram\n",
    "m = UNITS.meter\n",
    "s = UNITS.second\n",
    "N = UNITS.newton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [],
   "source": [
    "condition = Condition(mass = 0.03 * kg,\n",
    "                      fraction = 1 / 3,\n",
    "                      k = 9810.0 * N / m,\n",
    "                      duration = 0.3 * s,\n",
    "                      L = 0.05 * m,\n",
    "                      d = 0.005 * m,\n",
    "                      v1 = 0 * m / s,\n",
    "                      v2 = 0 * m / s,\n",
    "                      g = 9.8 * m / s**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "condition = Condition(mass = 0.03,\n",
    "                      fraction = 1 / 3,\n",
    "                      k = 9810.0,\n",
    "                      duration = 0.3,\n",
    "                      L = 0.05,\n",
    "                      d = 0.005,\n",
    "                      v1 = 0,\n",
    "                      v2 = 0,\n",
    "                      g = 9.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_system(condition):\n",
    "    \"\"\"Make a system object.\n",
    "    \n",
    "    condition: Condition with \n",
    "    \n",
    "    returns: System with init\n",
    "    \"\"\"\n",
    "    unpack(condition)\n",
    "    \n",
    "    x1 = L - d    # upper mass\n",
    "    x2 = 0        # lower mass  \n",
    "    \n",
    "    init = State(x1=x1, x2=x2, v1=v1, v2=v2)\n",
    "    \n",
    "    m1, m2 = fraction*mass, (1-fraction)*mass\n",
    "    ts = linspace(0, duration, 1001)\n",
    "    \n",
    "    return System(init=init, m1=m1, m2=m2, k=k, L=L, ts=ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `make_system`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>init</th>\n",
       "      <td>x1    0.045\n",
       "x2    0.000\n",
       "v1    0.000\n",
       "v2    0.00...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m1</th>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>m2</th>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k</th>\n",
       "      <td>9810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L</th>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ts</th>\n",
       "      <td>[0.0, 0.0003, 0.0006, 0.0009, 0.0012, 0.0015, ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "init    x1    0.045\n",
       "x2    0.000\n",
       "v1    0.000\n",
       "v2    0.00...\n",
       "m1                                                   0.01\n",
       "m2                                                   0.02\n",
       "k                                                    9810\n",
       "L                                                    0.05\n",
       "ts      [0.0, 0.0003, 0.0006, 0.0009, 0.0012, 0.0015, ...\n",
       "dtype: object"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = make_system(condition)\n",
    "system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>0.045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v1</th>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2</th>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x1    0.045\n",
       "x2    0.000\n",
       "v1    0.000\n",
       "v2    0.000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.init"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"Computes the derivatives of the state variables.\n",
    "    \n",
    "    state: State object with theta, y, r\n",
    "    t: time\n",
    "    system: System object with r, k\n",
    "    \n",
    "    returns: sequence of derivatives\n",
    "    \"\"\"\n",
    "    x1, x2, v1, v2 = state\n",
    "    unpack(system)\n",
    "    \n",
    "    dx = x1 - x2\n",
    "    f_spring = k * (L - dx)\n",
    "    \n",
    "    a1 = f_spring/m1 - g\n",
    "    a2 = -f_spring/m2 - g\n",
    "    \n",
    "    if t < 0.003 and a2 < 0:\n",
    "        a2 = 0\n",
    "    \n",
    "    return v1, v2, a1, a2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `slope_func`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0, 4895.199999999998, 0)"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_func(system.init, 0, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [],
   "source": [
    "run_odeint(system, slope_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>v1</th>\n",
       "      <th>v2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.2988</th>\n",
       "      <td>0.108655</td>\n",
       "      <td>0.055882</td>\n",
       "      <td>-3.678405</td>\n",
       "      <td>-0.058611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2991</th>\n",
       "      <td>0.107446</td>\n",
       "      <td>0.055916</td>\n",
       "      <td>-4.321706</td>\n",
       "      <td>0.258630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2994</th>\n",
       "      <td>0.106102</td>\n",
       "      <td>0.056017</td>\n",
       "      <td>-4.565052</td>\n",
       "      <td>0.375893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2997</th>\n",
       "      <td>0.104750</td>\n",
       "      <td>0.056120</td>\n",
       "      <td>-4.376955</td>\n",
       "      <td>0.277434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3000</th>\n",
       "      <td>0.103517</td>\n",
       "      <td>0.056163</td>\n",
       "      <td>-3.782438</td>\n",
       "      <td>-0.024235</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              x1        x2        v1        v2\n",
       "0.2988  0.108655  0.055882 -3.678405 -0.058611\n",
       "0.2991  0.107446  0.055916 -4.321706  0.258630\n",
       "0.2994  0.106102  0.056017 -4.565052  0.375893\n",
       "0.2997  0.104750  0.056120 -4.376955  0.277434\n",
       "0.3000  0.103517  0.056163 -3.782438 -0.024235"
      ]
     },
     "execution_count": 404,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.results.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GIvift64iMBSB3aLH57YugU6jVmx3c1gNKLQZ8M7ZTqk6lyAIWFSSHvCJ5jOz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd4bf413780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(system.results.x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mqlFk1CIzNQldA6PI0CWx2htRmGXrkxEfJ4Pb44N91IXB4XGoEuNxvnUQggAs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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd4bf445240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(system.results.x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h16aYx1VTCn5GKROr/GvinVF9zFD5X4+OamFA3Vv2c/L5yALkngzVbTGYCa1s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\nZJCUf4IECRIkSNBk8P8BwAYqZsPJv20AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd4bf2f7208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(system.results.x1 - system.results.x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(ys, color='green', label='y')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Length (m)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `r`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(rs, color='red', label='r')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Radius (mm)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also see the relationship between `y` and `r`, which I derive analytically in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(rs, ys, color='purple')\n",
    "\n",
    "decorate(xlabel='Radius (mm)',\n",
    "         ylabel='Length (m)',\n",
    "         legend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the figure from the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "subplot(3, 1, 1)\n",
    "plot(thetas, label='theta')\n",
    "decorate(ylabel='Angle (rad)')\n",
    "\n",
    "subplot(3, 1, 2)\n",
    "plot(ys, color='green', label='y')\n",
    "decorate(ylabel='Length (m)')\n",
    "\n",
    "subplot(3, 1, 3)\n",
    "plot(rs, color='red', label='r')\n",
    "\n",
    "decorate(xlabel='Time(s)',\n",
    "         ylabel='Radius (mm)')\n",
    "\n",
    "savefig('chap11-fig01.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use interpolation to find the time when `y` is 47 meters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "T = interp_inverse(ys, kind='cubic')\n",
    "t_end = T(47)\n",
    "t_end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At that point `r` is 55 mm, which is `Rmax`, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "R = interpolate(rs, kind='cubic')\n",
    "R(t_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total amount of rotation is 1253 rad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "THETA = interpolate(thetas, kind='cubic')\n",
    "THETA(t_end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unrolling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For unrolling the paper, we need more units:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kg = UNITS.kilogram\n",
    "N = UNITS.newton"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a few more parameters in the `Condition` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "condition = Condition(Rmin = 0.02 * m,\n",
    "                      Rmax = 0.055 * m,\n",
    "                      Mcore = 15e-3 * kg,\n",
    "                      Mroll = 215e-3 * kg,\n",
    "                      L = 47 * m,\n",
    "                      tension = 2e-4 * N,\n",
    "                      duration = 180 * s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`make_system` computes `rho_h`, which we'll need to compute moment of inertia, and `k`, which we'll use to compute `r`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_system(condition):\n",
    "    \"\"\"Make a system object.\n",
    "    \n",
    "    condition: Condition with Rmin, Rmax, Mcore, Mroll,\n",
    "                              L, tension, and duration\n",
    "    \n",
    "    returns: System with init, k, rho_h, Rmin, Rmax,\n",
    "                         Mcore, Mroll, ts\n",
    "    \"\"\"\n",
    "    unpack(condition)\n",
    "    \n",
    "    init = State(theta = 0 * radian,\n",
    "                 omega = 0 * radian/s,\n",
    "                 y = L)\n",
    "    \n",
    "    area = pi * (Rmax**2 - Rmin**2)\n",
    "    rho_h = Mroll / area\n",
    "    k = (Rmax**2 - Rmin**2) / 2 / L / radian    \n",
    "    ts = linspace(0, duration, 101)\n",
    "    \n",
    "    return System(init=init, k=k, rho_h=rho_h,\n",
    "                  Rmin=Rmin, Rmax=Rmax,\n",
    "                  Mcore=Mcore, Mroll=Mroll, \n",
    "                  ts=ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `make_system`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system = make_system(condition)\n",
    "system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system.init"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how we compute `I` as a function of `r`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def moment_of_inertia(r, system):\n",
    "    \"\"\"Moment of inertia for a roll of toilet paper.\n",
    "    \n",
    "    r: current radius of roll in meters\n",
    "    system: System object with Mcore, rho, Rmin, Rmax\n",
    "    \n",
    "    returns: moment of inertia in kg m**2\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    Icore = Mcore * Rmin**2   \n",
    "    Iroll = pi * rho_h / 2 * (r**4 - Rmin**4)\n",
    "    return Icore + Iroll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When `r` is `Rmin`, `I` is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "moment_of_inertia(system.Rmin, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As `r` increases, so does `I`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "moment_of_inertia(system.Rmax, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the slope function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"Computes the derivatives of the state variables.\n",
    "    \n",
    "    state: State object with theta, omega, y\n",
    "    t: time\n",
    "    system: System object with Rmin, k, Mcore, rho_h, tension\n",
    "    \n",
    "    returns: sequence of derivatives\n",
    "    \"\"\"\n",
    "    theta, omega, y = state\n",
    "    unpack(system)\n",
    "    \n",
    "    r = sqrt(2*k*y + Rmin**2)\n",
    "    I = moment_of_inertia(r, system)\n",
    "    tau = r * tension\n",
    "    alpha = tau / I\n",
    "    dydt = -r * omega\n",
    "    \n",
    "    return omega, alpha, dydt      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `slope_func`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "slope_func(system.init, 0*s, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "run_odeint(system, slope_func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And look at the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system.results.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extrating the time series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "thetas = system.results.theta\n",
    "omegas = system.results.omega\n",
    "ys = system.results.y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `theta`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(thetas, label='theta')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angle (rad)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `omega`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(omegas, color='orange', label='omega')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angular velocity (rad/s)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(ys, color='green', label='y')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Length (m)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the figure from the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "subplot(3, 1, 1)\n",
    "plot(thetas, label='theta')\n",
    "decorate(ylabel='Angle (rad)')\n",
    "\n",
    "subplot(3, 1, 2)\n",
    "plot(omegas, color='orange', label='omega')\n",
    "decorate(ylabel='Angular velocity (rad/s)')\n",
    "\n",
    "subplot(3, 1, 3)\n",
    "plot(ys, color='green', label='y')\n",
    "\n",
    "decorate(xlabel='Time(s)',\n",
    "         ylabel='Length (m)')\n",
    "\n",
    "savefig('chap11-fig02.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Yo-yo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Simulate the descent of a yo-yo.  How long does it take to reach the end of the string.\n",
    "\n",
    "I provide a `Condition` object with the system parameters:\n",
    "\n",
    "* `Rmin` is the radius of the axle.  `Rmax` is the radius of the axle plus rolled string.\n",
    "\n",
    "* `Rout` is the radius of the yo-yo body.  `mass` is the total mass of the yo-yo, ignoring the string.  \n",
    "\n",
    "* `L` is the length of the string.\n",
    "\n",
    "* `g` is the acceleration of gravity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "condition = Condition(Rmin = 8e-3 * m,\n",
    "                      Rmax = 16e-3 * m,\n",
    "                      Rout = 35e-3 * m,\n",
    "                      mass = 50e-3 * kg,\n",
    "                      L = 1 * m,\n",
    "                      g = 9.8 * m / s**2,\n",
    "                      duration = 1 * s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a `make_system` function that computes `I` and `k` based on the system parameters.\n",
    "\n",
    "I estimated `I` by modeling the yo-yo as a solid cylinder with uniform density ([see here](https://en.wikipedia.org/wiki/List_of_moments_of_inertia)).  In reality, the distribution of weight in a yo-yo is often designed to achieve desired effects.  But we'll keep it simple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_system(condition):\n",
    "    \"\"\"Make a system object.\n",
    "    \n",
    "    condition: Condition with Rmin, Rmax, Rout, \n",
    "                              mass, L, g, duration\n",
    "    \n",
    "    returns: System with init, k, Rmin, Rmax, mass,\n",
    "                         I, g, ts\n",
    "    \"\"\"\n",
    "    unpack(condition)\n",
    "    \n",
    "    init = State(theta = 0 * radian,\n",
    "                 omega = 0 * radian/s,\n",
    "                 y = L,\n",
    "                 v = 0 * m / s)\n",
    "    \n",
    "    I = mass * Rout**2 / 2\n",
    "    k = (Rmax**2 - Rmin**2) / 2 / L / radian    \n",
    "    ts = linspace(0, duration, 101)\n",
    "    \n",
    "    return System(init=init, k=k,\n",
    "                  Rmin=Rmin, Rmax=Rmax,\n",
    "                  mass=mass, I=I, g=g,\n",
    "                  ts=ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `make_system`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system = make_system(condition)\n",
    "system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system.init"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a slope function for this system, using these results from the book:\n",
    "\n",
    "$ r = \\sqrt{2 k y + R_{min}^2} $ \n",
    "\n",
    "$ T      = m g I / I^*  $\n",
    "\n",
    "$ a      = -m g r^2 / I^* $\n",
    "\n",
    "$ \\alpha  = m g r / I^*  $\n",
    "\n",
    "where $I^*$ is the augmented moment of inertia, $I + m r^2$.\n",
    "\n",
    "Hint: If `y` is less than 0, it means you have reached the end of the string, so the equation for `r` is no longer valid.  In this case, the simplest thing to do it return the sequence of derivatives `0, 0, 0, 0`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your slope function with the initial conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "slope_func(system.init, 0*s, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then run the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "run_odeint(system, slope_func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the final conditions.  If things have gone according to plan, the final value of `y` should be close to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "system.results.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "thetas = system.results.theta\n",
    "ys = system.results.y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`theta` should increase and accelerate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(thetas, label='theta')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angle (rad)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`y` should decrease and accelerate down."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot(ys, color='green', label='y')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Length (m)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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